Abstract: The nonlinear analytic nodal method require analytic solutions of the two-node problems,in which the numerical instability problem might be encountered due to the ill-conditioned algorithm for finding the particular solution of near-critical node.To address this problem,a stabilization method is developed by applying the method of variation of parameters and linear approximation to the near-critical node calculations.Numerical results demonstrate the effectiveness of the method.

Key words: numerical stability, analytic nodal method, nonlinear iteration